Question

What is the maximum number of emission lines when the excited electron of a hydrogen atom in n = 6 drops to ground state?
A. 6
B. 15
C. 30
D. 10

Answer 1

When an electron absorbs energy it becomes excited and jumps from lower energy level to higher energy level and when it comes back to its ground state, the same amount of energy is released as was absorbed when it went to higher energy level.

Complete answer:
When an electron in a higher energy state jumps to a lower energy state in Bohr’s model of hydrogen atom, it emits a photon which has energy equal to the difference in the energy between the final and initial energy states.
$h\nu = {E_f} - {E_i}$
Where, $\nu$= frequency of photon emitted
Each photon emitted corresponds to an emission line in the spectrum.
So, an electron can make the transition from a higher energy state to any lower energy state provided it emits a photon given by the above equation. In the question given, if an electron is in a higher energy state; the maximum number of spectral lines is when the electron jumps to the next lowest energy state and so on as then photons will be emitted during each transition.
When an electron in the first energy level of a Hydrogen atom absorbs energy, it becomes excited and jumps to ${6^{th}}$ energy level. When it returns back, it can return straight back to the first energy level or in several steps. The following transitions may be possible, that is,
It can jump from$6 \to 5,6 \to 4,6 \to 3,6 \to 2,6 \to 1[5steps]$
or from $6 \to 4,6 \to 3,6 \to 2,6 \to 1$ (4 steps)
and so on till it reaches the single step transition
That is, from $6 \to 1$
Hence, total lines obtained on the emission spectrum will be$(5 + 4 + 3 + 2 + 1) = 15lines$
The number of spectral lines can also be found by the formula given by Neil Bohr as follows:
According to Bohr’s Model of Hydrogen spectrum,
The number of spectral lines formed when electron jump or drop from the ${n^{th}}$level to ground level = $\dfrac{{n(n - 1)}}{2}$
here $n = 6$
So, $\dfrac{{6(6 - 1)}}{2} = 15$

Hence, the answer is option B which is 15 is correct.

Note: Remember that an excited electron can return back directly and also in several steps. However, once it returns to its ground state, the energy released will be the same.